Abstract: We present a highly complete and reliable mid-infrared (MIR) colour selection of luminous active galactic nucleus (AGN) candidates using the 3.4, 4.6 and 12 µm bands of the Wide- field Infrared Survey Explorer (WISE) survey. The MIR colour wedge was defined using the wide-angle Bright Ultrahard XMM?Newton survey (BUXS), one of the largest complete flux-limited samples of bright (f4.5?10 keV > 6 10?14 erg s?1 cm?2) ?ultrahard? (4.5?10 keV) X-ray-selected AGN to date. The BUXS includes 258 objects detected over a total sky area of 44.43 deg2 of which 251 are spectroscopically identified and classified, with 145 being type 1 AGN and 106 type 2 AGN. Our technique is designed to select objects with red MIR power-law spectral energy distributions (SEDs) in the three shortest bands of WISE and properly accounts for the errors in the photometry and deviations of the MIR SEDs from a pure power-law. The completeness of the MIR selection is a strong function of luminosity. At L2?10 keV > 1044 erg s?1, where the AGN is expected to dominate the MIR emission, 97.1+2.2 and 76 5+13.3 ?4.8 . 18.4 per cent of the BUXS type 1 and type 2 AGN, respectively, meet the selection. Our technique shows one of the highest reliability and efficiency of detection of the X-ray- selected luminous AGN population with WISE amongst those in the literature. In the area covered by BUXS our selection identifies 2755 AGN candidates detected with signal-to-noise ratio 5 in the three shorter wavelength bands of WISE with 38.5 per cent having a detection at 2?10 keV X-ray energies. We also analysed the possibility of including the 22 µm WISE band to select AGN candidates, but neither the completeness nor the reliability of the selection

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